Abstract
We prove the existence of a fundamental solution of the Cauchy initial boundary value problem on the whole space for a parabolic partial differential equation with discontinuous unbounded first-order coefficient at the origin. We establish also non-asymptotic, rapidly decreasing at infinity, upper and lower estimates for the fundamental solution. We extend the classical parametrix method of E.E. Levi.
Original language | English |
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Pages (from-to) | 399-413 |
Number of pages | 15 |
Journal | Acta Applicandae Mathematicae |
Volume | 170 |
Issue number | 1 |
DOIs | |
State | Published - 1 Dec 2020 |
Bibliographical note
Funding Information:The first author has been partially supported by the Gruppo Nazionale per l’Analisi Matematica, la Probabilità e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and by Università degli Studi di Napoli Parthenope through the project “sostegno alla Ricerca individuale”.
Funding Information:
The first author has been partially supported by the Gruppo Nazionale per l?Analisi Matematica, la Probabilit? e le loro Applicazioni (GNAMPA) of the Istituto Nazionale di Alta Matematica (INdAM) and by Universit? degli Studi di Napoli Parthenope through the project ?sostegno alla Ricerca individuale?.
Publisher Copyright:
© 2020, Springer Nature B.V.
Keywords
- Chapman-Kolmogorov equation
- Fundamental solution
- Generalized Mittag-Leffler function
- Neumann series
- Partial Differential Equation of parabolic type
- Volterra’s integral equation